Abstract

Mie theory offers an exact solution to the problem of scattering of sunlight by spherical drops of water. Until recently, most applications of Mie theory to scattering of light were restricted to a single wavelength. Mie theory can now be used on modern personal computers to produce full-color simulations of atmospheric optical effects, such as rainbows, coronas, and glories. Comparison of such simulations with observations of natural glories and cloudbows is encouraging.

X. Han, “Study of refractometry of rainbow and applications to the measurement of instability and temperature gradient of a liquid jet,” Ph.D. dissertation (University of Rouen, Rouen, France, 2000), available at http://www.coria.fr/LESP/OP15/Han/TheseHan.htm .

International Association for the Properties of Water and Steam, “Release on the refractive index of ordinary water substance as a function of wavelength, temperature and pressure” (1997), http://www.iapws.org/relguide/rindex.pdf .

International Association for the Properties of Water and Steam, “Release on the refractive index of ordinary water substance as a function of wavelength, temperature and pressure” (1997), http://www.iapws.org/relguide/rindex.pdf .

X. Han, “Study of refractometry of rainbow and applications to the measurement of instability and temperature gradient of a liquid jet,” Ph.D. dissertation (University of Rouen, Rouen, France, 2000), available at http://www.coria.fr/LESP/OP15/Han/TheseHan.htm .

(a) Graph of intensity versus scattering angle θ. r = 100 μm, λ = 0.65 μm, n = 1.332, perpendicular polarization. (b) As in (a) but intensity is the average intensity of scattering by 50 spheres with different values of radius with a log-normal distribution with a median radius of 100 μm and a standard deviation of 0.1 μm (0.1% of the median radius). (c) As in (a) but intensity is averaged to take account of the 0.5° diameter of the Sun.

(a) Simulation of primary and secondary rainbows caused by scattering of unpolarized sunlight from r = 100 μm water drops with the specified number N of wavelengths. (b) As in (a) but limited to the secondary rainbow.